A note on thick subcategories of stable derived categories

Preprint, Other literature type English OPEN
Krause, Henning ; Stevenson, Greg (2013)
  • Publisher: Duke University Press
  • Journal: (issn: 0027-7630)
  • Related identifiers: doi: 10.1215/00277630-2351125
  • Subject: 13D09 | Mathematics - Category Theory | 14F05 | 18E30 | Mathematics - Commutative Algebra | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Representation Theory | Mathematics::Algebraic Geometry | Mathematics::Category Theory

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection, we classify thick subcategories of finitely gener... View more
  • References (19)
    19 references, page 1 of 2

    [1] P. Balmer and M. Schlichting, Idempotent completion of triangulated categories, J. Algebra 236 (2001), no. 2, 819-834.

    [2] A. Beligiannis and H. Krause, Thick subcategories and virtually Gorenstein algebras, Illinois J. Math. 52 (2008), no. 2, 551-562.

    [3] D. J. Benson, J. F. Carlson and J. Rickard, Thick subcategories of the stable module category, Fund. Math. 153 (1997), no. 1, 59-80.

    [4] D. J. Benson, S. B. Iyengar, and H. Krause, Stratifying modular representations of finite groups, Ann. of Math. (1) 174 (2011); to appear, arxiv:0810.1339.

    [5] A. Bondal and M. Van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003), no. 1, 1-36, 258.

    [6] R.-O. Buchweitz, Maximal Cohen-Macaulay modules and Tate-cohomology over Gorenstein rings, Unpublished manuscript (1987), 155 pp.

    [7] R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag

    [8] H. Krause, The stable derived category of a Noetherian scheme, Compos. Math. 141 (2005), no. 5, 1128-1162.

    [9] A. Neeman, The derived category of an exact category, J. Algebra 135 (1990), no. 2, 388-394.

    [10] A. Neeman, The connection between the K-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel, Ann. Sci. EĀ“cole Norm. Sup. (4) 25 (1992), no. 5, 547-566.

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